Q: Subgroup of rotations in $D_n$ is normal. Here is what I did:
Suppose R $\leq$ $D_n$ is the subgroup of rotation. Suppose $x \in fRf^{-1}$. Then $x = frf^{-1}$ for some r and for any r. Therefore, $x = r'$ a rotation and hence $x \in R$. therefore by definition R is normal in $D_n$
Is this correct and complete verification?
Thanks, any other suggestions??

A: Well, it is correct. But you should emphasize and expand a bit more the essence of the thought, and this is:

Therefore $x=frf^{-1}$ is a rotation.

So.. Why is it a rotation? That's the point.
